Passage: Two volatile liquids A and B form an ideal solution. Consider a 5 molal solution of B in A inside a closed container having a total vapour pressure of 100 mm Hg at 300 K. The vapour pressure of pure A at 300 K is 105 mm Hg. Assume that A and B behave as ideal gases in the vapour phase. Give

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Passage: Two volatile liquids A and B form an ideal solution. Consider a 5 molal solution of B in A inside a closed container having a total vapour pressure of 100 mm Hg at 300 K. The vapour pressure of pure A at 300 K is 105 mm Hg. Assume that A and B behave as ideal gases in the vapour phase. Given: The gas constant R = 0.08 L atm K^ -1 mol^ -1 Molar mass of A is 50 g mol^ -1 Molar mass of B is 57 g mol^ -1 Density of liquid B at 300 K is 0.5 g/mL 1 atm = 760 mm Hg Question: At 300 K, the ratio of the molar volume of pure B in vapour phase to its molar volume in liquid phase is ____.

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Correct answer: A. A

For a 5 molal solution of B in A, there are 5 moles of B in 1000 g of A. Moles of A = 1000 50 = 20 mol. Mole fraction of B, x_B = 5 20 + 5 = 0.2 Mole fraction of A, x_A = 1 - 0.2 = 0.8 Using Raoult's law for the total vapour pressure: P_T = P_A^ x_A + P_B^ x_B 100 = 105 0.8 + P_B^ 0.2 100 = 84 + 0.2 P_B^ 0.2 P_B^ = 16 P_B^ = 80 mm Hg The molar volume of pure B in the liquid phase (V_ m,l ) is: V_ m,l = Molar mass of B Density of liquid B = 57 0.5 = 114 mL/mol = 0.114 L/mol Assuming pure B behaves as an ideal gas in the vapour phase, its molar volume (V_ m,v ) at its vapour pressure P_B^ is: V_ m,v = RT P_B^ = 0.08 300 ( 80 760 ) = 24 760 80 = 228 L/mol The ratio of the molar volume of pure B in the vapour phase to its molar volume in the liquid phase is: Ratio = V_ m,v V_ m,l = 228 0.114 = 2000 Answer: 2000

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